With your semantics, yes "viral elimination" is possible. However, HIV does not live as a virus in the body until just before it breaks from the cell and is released. HIV lives as an integrated part of your DNA in infected cells.
If ozone works (not saying it does or does not), and if you can get it into the cell, it can kill the viruses that the cell is making. This does NOT mean you are killing the HIV though, because the Ozone will not destroy the cell's DNA (which is where the HIV lives). This is the problem and beauty with HIV and other RT parasites. They can integrate themselves with a host, without killing the host for long periods of time, leading to better chances of infecting another host and survival of the virus. And since they are integrated with the host DNA, the only way of killing the virus is to kill the host as well. In evolutionary terms, HIV is one of the best viruses nature can create, which is what makes it so problematic.
Now, many things can be done to keep your viral load low and your disease under control, but HIV can never be "cured". This is not to be all doom and gloom, you can live an almost normal life with HIV if you treat it correctly. However, the ONLY way to live without HIV is to never have gotten it in the first place.
This is wrong on several points. HIV can be destroyed by ozone because of its lipid envelope. Ozone reacts with this lipid envelope forming a lipid peroxide, destroying the virus in the process.
As for it being the "best viruses nature can create" it was not nature that created it. It was man that created it. The request for the production of the HIV virus is public record. Look at the Senate Subcommittee Hearings for Chemical Biological Warfare Appropriations for 1970, Part 6, July 1, 1969 page 1 for the request for its production by the US government. For the information on introducing this and other deadly manmade viruses through vaccine programs starting in Africa in the late 70s, when and where this all began you will also need to read the Bull WHO 1972 and the Federation Proceedings 1972 (sponsored by the WHO). This is where they not only talk about specifically making synthetic viruses that will wipe out either T cell (CD4 cells), B cells or antibody production, but leaving the rest of the immune system intact, but also deliberately introducing these man-made viruses through routine vaccinations. These are their words, not mine. Also note that all the first cases of AIDS in Africa started when the WHO started their Expanded Program on Immunization (EPI) and in the villages receiving the vaccines. The first cases in Haiti occurred in the 18,000 Haitians working on the vaccine program that were themselves immunized. The first cases in the US were all in homosexual and bisexual men recruited for experimental hepatitis vaccines starting in the late 70s. This was pointed out in several articles published in the medical journal Journal of the American Medical Association. Another interesting fact that can also be verified with a little research is that the men recruited for the experimental hepatitis vaccines had to be under the age of 40 to participate. And according to the ORIGINAL definition of AIDS set by the CDC, the CDC claimed that a person could not have AIDS if they were over the age of 40. Kind of interesting that they would say this being that they supposedly did not know much of anything about AIDS when it first appeared. This is just the tip of the iceberg. There is so much overwhelming evidence that HIV was not only produced by the US government, but we also played a major role in its introduction.